A Five-Point Subdivision Scheme with Two Parameters and a Four-Point Shape-Preserving Scheme

Tan, Jieqing; Wang, Bo; Shi, Jun

doi:10.3390/mca22010022

Cited by 3 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 2017, Feng et al [13] presented a family of non-uniform schemes with variable parameters. Tan et al [14] presented a new 5-point binary approximating scheme with two parameters in 2017. In 2018, Asghar and Mustafa [15] presented a family of a-ary univariate subdivision schemes with single parameter.…”

Section: Introductionmentioning

confidence: 99%

A Class of Refinement Schemes With Two Shape Control Parameters

et al. 2020

View full text Add to dashboard Cite

A subdivision scheme defines a smooth curve or surface as the limit of a sequence of successive refinements of given polygon or mesh. These schemes take polygons or meshes as inputs and produce smooth curves or surfaces as outputs. In this paper, a class of combine refinement schemes with two shape control parameters is presented. These even and odd rules of these schemes have complexity three and four respectively. The even rule is designed to modify the vertices of the given polygon, whereas the odd rule is designed to insert a new point between every edge of the given polygon. These schemes can produce high order of continuous shapes than existing combine binary and ternary family of schemes. It has been observed that the schemes have interpolating and approximating behaviors depending on the values of parameters. These schemes have an interproximate behavior in the case of non-uniform setting of the parameters. These schemes can be considered as the generalized version of some of the interpolating and B-spline schemes. The theoretical as well as the numerical and graphical analysis of the shapes produced by these schemes are also presented.

show abstract

Section: Introductionmentioning

confidence: 99%

A Class of Refinement Schemes With Two Shape Control Parameters

et al. 2020

View full text Add to dashboard Cite

show abstract

A Study on the Class of Non-Symmetric 3-Point Relaxed Quaternary Subdivision Schemes

2022

View full text Add to dashboard Cite

Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme

et al. 2020

View full text Add to dashboard Cite

In this paper, we analyze shape-preserving behavior of a relaxed four-point binary interpolating subdivision scheme. These shape-preserving properties include positivity-preserving, monotonicity-preserving and convexity-preserving. We establish the conditions on the initial control points that allow the generation of shape-preserving limit curves by the four-point scheme. Some numerical examples are given to illustrate the graphical representation of shape-preserving properties of the relaxed scheme.

show abstract

A Five-Point Subdivision Scheme with Two Parameters and a Four-Point Shape-Preserving Scheme

Cited by 3 publications

References 14 publications

A Class of Refinement Schemes With Two Shape Control Parameters

A Class of Refinement Schemes With Two Shape Control Parameters

A Study on the Class of Non-Symmetric 3-Point Relaxed Quaternary Subdivision Schemes

Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme

Contact Info

Product

Resources

About